{"paper":{"title":"Weak Dirichlet processes with jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Elena Bandini (ENSTA ParisTech UMA), Francesco Russo (ENSTA ParisTech UMA)","submitted_at":"2015-12-19T12:31:39Z","abstract_excerpt":"This paper develops systematically the stochastic calculus via regularization in the case of jump processes. In particular one continues  the analysis of real-valued c\\`adl\\`ag weak Dirichlet processes with respect to a given filtration. Such a process is the sum of a local martingale and an adapted process $A$ such that $[N,A] = 0$, for any continuous local martingale $N$. Given a  function $u:[0,T] \\times \\mathbb{R} \\to \\mathbb{R}$, which is of   class $C^{0,1}$ (or sometimes less), we provide a chain  rule type expansion for $u(t,X_t)$  which stands in applications  for a chain It\\^o type r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06236","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}